An integrated firefly algorithm for the optimization of constrained engineering design problems

Abstract As a nature-inspired metaheuristic method, the firefly algorithm (FA) arises more attentions in academic and engineering fields. However, the computational efficiency and accuracy of FA still need improvement to deal with complex engineering problems. Thus, an integrated firefly algorithm (IFA) that combines two novel attractive models with a new stochastic model is proposed to improve the standard FA. Firstly, the attractive model and stochastic model of standard FA are investigated through theoretical analysis and numerical experiments. And the factors that affect the computational efficiency and accuracy of FA are revealed. Then, a fitness-based virtual attractive model and a fitness-based global best attractive model are constructed to reduce the computation complexity and enhance the exploitation ability. Moreover, an adaptive strategy is presented for the stochastic model to achieve a better balance between exploitation and exploration. Additionally, an adaptive penalty function method is developed to handle the constraints effectively. Then, the initial parameters are tested, and the best initial parameters corresponding to the optimal performance of IFA are obtained. Finally, IFA and other metaheuristic algorithms are applied to solve five engineering design optimization problems with mixed variables and multiple constraint conditions. The results indicate that IFA with adaptive penalty function needs fewer fitness evaluations and costs less computational time to obtain the optimal solutions. Furthermore, it exhibits better accuracy and robustness than other algorithms.